1991 mustang gt will turn over with no key

question for ya I have a 1991 mustang gt comvertible my ignition turns without a key last time it was on the road about 2010 if it sat over night id need a jump start every morning this was with a used auto wrecker battry since then I have bought a new battery but kept it un hooked and only hooked it up to idle the car once a month im putting it back on road in next couple months could the fact that it turns without a key be draining the battery ? I am planning to fix the issue but just wondering if I should look elsewhere for the battery drain issue